A378922 Number of minimal edge cuts in the n-antiprism graph.

1, 1, 7, 28, 81, 191, 391, 722, 1233, 1981, 3031, 4456, 6337, 8763, 11831, 15646, 20321, 25977, 32743, 40756, 50161, 61111, 73767, 88298, 104881, 123701, 144951, 168832, 195553, 225331, 258391, 294966, 335297, 379633, 428231, 481356, 539281, 602287, 670663, 744706, 824721

Offset

0,3

Comments

The n-antiprism graph is defined for n >= 3. The sequence has been extended to n = 0 using the formula. - Andrew Howroyd, Jun 09 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Antiprism Graph.

Eric Weisstein's World of Mathematics, Minimal Edge Cut.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

From Andrew Howroyd, Jun 09 2025: (Start)

a(n) = 1 + 2*n*(n-1) + n^2*(n-1)*(2*n-1)/6.

a(n) = (2*n^4 - 3*n^3 + 13*n^2 - 12*n + 6)/6. (End)

From Elmo R. Oliveira, Sep 03 2025: (Start)

G.f.: (1 - 4*x + 12*x^2 - 7*x^3 + 6*x^4)/(1-x)^5.

E.g.f.: (6 + 18*x^2 + 9*x^3 + 2*x^4)*exp(x)/6.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

Mathematica

Table[(6 - 12 n + 13 n^2 - 3 n^3 + 2 n^4)/6, {n, 0, 20}] (* Eric W. Weisstein, Oct 01 2025 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 1, 7, 28, 81}, 20] (* Eric W. Weisstein, Oct 01 2025 *)
CoefficientList[Series[(-1 + 4 x - 12 x^2 + 7 x^3 - 6 x^4)/(-1 + x)^5, {x, 0, 20}], x] (* Eric W. Weisstein, Oct 01 2025 *)

Prog

(PARI) a(n) = (2*n^4 - 3*n^3 + 13*n^2 - 12*n + 6)/6 \\ Andrew Howroyd, Jun 09 2025

Crossrefs

Cf. A359620.

Sequence in context: A024012 A352900 A163705 * A162595 A073363 A247608

Adjacent sequences: A378919 A378920 A378921 * A378923 A378924 A378925

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 11 2024

Extensions

a(0)-a(2) prepended and a(7) onwards from Andrew Howroyd, Jun 09 2025

Status

approved